What are we supposed to be seeing here? What difference between the two images do you consider to be significant?

It looks like text in a table. It appears in a red box when you compose, so as to assist you with placing text exactly where you want it.

Sorry I thought you were able to see the titles of the pictures. The left one is how it should look like and the right is how it's formatted in a reply.

The Signature is written in HTML that's why it looks like a table.

Well, yes, I can see two images that are slightly different. But I don't see what is "wrong" with the second one. It's different, but legible and says all the same things. Or am I continuing to miss something?

A reply to an html-formatted message may take settings embedded into the html of the message you're replying to. So line heights, font weights etc might be slightly different. If you really want to avoid these changes, you may have to play some tricks such as using "copy and paste without formatting" to impose your own choice of formatting.

When replying, the frames around signatures of original senders are all messed up (large white spaces with formatting characters) and can't be edited out (deleted). Is there a way to do it? Please help.

It's the ugliest when one needs to forward somebody's email, and detailed headers show up in frames and can't be deleted.

Here's a screenshot.

A) You can eliminate most of this. View|Headers|Normal

B) To remove a table, click in the table to select it. Then go to Format|Table|Delete|Table .